can we fetch other users information programmatically, by logging with different user Id.

This (owned work items etc) is not information related to permissions required to read individual user data such as the mail address. This is governed by other permissions and access restrictions.

This information can be retrieved using the Java API for example. Start here https://rsjazz.wordpress.com/2013/03/20/understanding-and-using-the-rtc-java-client-api/ and look for other posts e.g. on querying.

Provided the user has permission and access to get that data, you can use any user. The permission aware API also tells you if you don't have access to specific items.

what do you mean 'information'?

to show list of workitems by  user, create a query that shows those results. you can get both creator and owner

If you want count of workitems and not list, then you will have to write a report or some client code to execute the query.